Camden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 150 mg of sodium and each frozen dinner has 300 mg of sodium. Camden purchased a total of 7 cans of soup and frozen dinners which collectively contain 1500 mg of sodium. Graphically solve a system of equations in order to determine the number of cans of soup purchased, x, and the number of frozen dinners purchased, y.

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karizmasamplethe karizmasamplethe · Answer 1 · 2024-02-21T14:41:00+01:00

Answer:

Camden purchased 4 cans of soup and 3 frozen dinners.

Step-by-step explanation:

How to solve for this

We can solve this problem by using a system of two linear equations.

Let x be the number of cans of soup purchased and y be the number of frozen dinners purchased.

Then, based on the information given, we can set up two equations as follows:

150x + 300y = 1500 (the total amount of sodium consumed is 1500 mg)

x + y = 7 (Camden purchased 7 cans of soup and frozen dinners)

Now, we can use either substitution or elimination to find the values of x and y.

Using substitution:

Solve the second equation for y: y = 7 - x

Substitute the expression for y into the first equation: 150x + 300(7 - x) = 1500

Simplify the expression: 150x + 2100 - 300x = 1500

Combine like terms: -150x + 2100 = 1500

Solve for x: -150x = -600

Divide both sides by -150: x = 4

Use the second equation to find y: y = 7 - x = 7 - 4 = 3

So, Camden purchased 4 cans of soup and 3 frozen dinners.